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Research Papers

Adhesion Between Thin Cylindrical Shells With Parallel Axes

[+] Author and Article Information
Carmel Majidi1

Princeton Institute for the Science and Technology of Materials, Princeton University, Princeton, NJ 08544cmajidi@princeton.edu

Kai-tak Wan2

Mechanical and Industrial Engineering, Northeastern University, Boston, MA 02115ktwan@coe.neu.edu

1

Current address: School of Engineering and Applied Sciences (SEAS), Harvard University, Cambridge, MA 02138.

2

Corresponding author.

J. Appl. Mech 77(4), 041013 (Apr 14, 2010) (10 pages) doi:10.1115/1.4000924 History: Received July 02, 2009; Revised October 05, 2009; Published April 14, 2010; Online April 14, 2010

Energy principles are used to investigate the adhesion of two parallel thin cylindrical shells under external compressive and tensile loads. The total energy of the system is found by adding the strain energy of the deformed cylinder, the potential energy of the external load, and the surface energy of the adhesion interface. The elastic solution is obtained by linear elastic plate theory and a thermodynamic energy balance, and is capable of portraying the measurable quantities of external load, stack height, contact arc length, and deformed profile in the reversible process of loading-adhesion and unloading-delamination. Several worked examples are given as illustrations. A limiting case of adhering identical cylinders is shown to be consistent with recent model constructed by Tang et al. Such results are of particular importance in modeling the aggregation of heterogeneous carbon nanotubes or cylindrical cells, where the contacting microstructures have a different radius and/or bending stiffness.

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Copyright © 2010 by American Society of Mechanical Engineers
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References

Figures

Grahic Jump Location
Figure 5

Adhesion between two cylindrical shells with the same radii (R1=R2=1) but different bending stiffnesses (k1=1,k2=0.5) under a compressive load F for γ=3 (unless indicated otherwise). (a) Deformed profile. (b) Half arc contact length as a function of compressive load. (c) Compressive load F as a function of compression distance w, with the dashed line indicating line contact (a=0) where adhesion has no influence.

Grahic Jump Location
Figure 4

Adhesion between two cylindrical shells with the same bending stiffness (k1=k2=1) but different radii (R1=1,R2=0.5) under a compressive load F for γ=3 (unless indicated otherwise). (a) Deformed profile. (b) Half contact arc length as a function of compressive load. (c) Compressive load F as a function of compression distance w, with the dashed line indicating line contact (a=0) where adhesion has no influence.

Grahic Jump Location
Figure 3

Adhesion between two identical cylindrical shells with the same bending stiffness (k1=k2=1) and radii (R1=R2=1) under a compressive load F for γ=3 (unless indicated otherwise). (a) Deformed profile with pole of bottom cylinder as reference. (b) Half contact arc length as a function of compressive load. (c) Compressive load F as a function of compression distance w, with the dashed line indicating line contact (a=0) where adhesion has no influence on the interacting cylinders.

Grahic Jump Location
Figure 2

Curvilinear coordinates

Grahic Jump Location
Figure 1

Interactions between two cylindrical shells: (a) touching at a line contact without adhesion, (b) compressive deformation with adhesion, and (c) tensile deformation with adhesion

Grahic Jump Location
Figure 7

Threshold radius for line contact (a=0) as function of stiffness and adhesion energy. (Rmin=(k/γ)1/2 for R1=R2=R and k1=k2=k.)

Grahic Jump Location
Figure 6

Normalized pull-off strength F0 as a function of adhesion energy γ. (a) Same radius (R1=R2=1), but different stiffness with k1=1. (b) Same stiffness (k1=k2=1), but different radii with R1=1.

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